What is wrong with my a/c condenser if it buzzes but won't start?

Your A/C condensor's motor does not have power to the starter winding(s);
either the centrifugal (starter) switch or the starter capacitor is not working.
If (commercial/industrial) 3-phase delta or wye power,
then 1 or 2 of the 3 electrical supply phases are out at the motor,
usually caused by either a utility company issue or a bad starter contactor/relay.

Could have a bad voltage regulator.If the air conditioner has not been used for a period of time it could have seized the electric motor's.If air conditioner is 1-2 years or older could need freon refill if the blower works but just a buzzing sound from the condensor could be a ballast inside gone bad.

This problem is usually caused by a bad contactor.With age, the contacts become worn and get stuck together causing a loud buzzing noise.The other cause could be a burned out fan motor on the unit.If the fan is moving,then more then likely the contactor is what needs to be replaced.

Humming generally indicates an electrical issue. On a condenser unit it could be either the motor itself or a contactor/capacitor. The motor is going to be a more expensive option. I would replace the start/run capacitor first.

It sounds like the motor is burned out or jammed. The buzz is probably the electric motor trying to spin the blades, but can't. Something may have gotten wedged in. You can make sure the power to it is turned off and examine the unit yourself, or call a repairman before the summer heats up.

Your-air-conditioner-compressor "buzzing" probably means that its motor has either:
bad-starter-capacitor, failed-windings/insulation, or bad-starter-relay.
Measure your-refrigerant-line high & low side-pressure or temperature
to check for refrigerant-leaks before & after replacing compressor.